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Support vector machine (SVM) has been shown powerful in binary classification problems. In order to accommodate SVM to speaker verification problem, the concept of sequence kernel has been developed, which maps variable-length speech data into fixed-dimension vectors. However, constructing a suitable sequence kernel for speaker verification is still an issue. In this paper, we propose a new sequence kernel, named the log-likelihood ratio (LLR)-based sequence kernel, to incorporate LLR-based speaker verification approaches into SVM without needing to represent variable-length speech data as fixed-dimension vectors in advance. Our experimental results show that the proposed sequence kernels outperform the conventional kernel-based approaches.